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%I #63 Feb 20 2023 22:08:38
%S 0,0,0,0,0,0,0,0,0,0,1,1,3,8,25,88,378,2026,13351,104595,930586,
%T 9124662,96699987,1095469608,13175272208,167460699184,2241578965849,
%U 31510542635443,464047929509794,7143991172244290,114749135506381940,1919658575933845129,33393712487076999918,603152722419661386031
%N Number of disconnected 4-valent (or quartic) graphs with n nodes.
%D R. C. Read and R. J. Wilson, An Atlas of Graphs, Oxford, 1998.
%H Jason Kimberley, <a href="/wiki/User:Jason_Kimberley/D_k-reg_girth_ge_g_index">Index of sequences counting disconnected k-regular simple graphs with girth at least g</a>
%H N. J. A. Sloane, <a href="/transforms.txt">Transforms</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DisconnectedGraph.html">Disconnected Graph</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/QuarticGraph.html">Quartic Graph</a>
%F a(n) = A033301(n) - A006820(n) = Euler_transformation(A006820) - A006820.
%F a(n) = A068933(n, 4). - _Jason Kimberley_, Sep 27 2009 and Jan 08 2011
%t A006820 = Cases[Import["https://oeis.org/A006820/b006820.txt", "Table"], {_, _}][[All, 2]];
%t (* EulerTransform is defined in A005195 *)
%t EulerTransform[Rest @ A006820] - A006820 (* _Jean-François Alcover_, Jan 21 2020, updated Mar 17 2020 *)
%Y 4-regular simple graphs: A006820 (connected), this sequence (disconnected), A033301 (not necessarily connected). - _Jason Kimberley_, Jan 08 2011
%Y Disconnected regular simple graphs: A068932 (any degree), A068933 (triangular array), specified degree k: A165652 (k=2), A165653 (k=3), this sequence (k=4), A165655 (k=5), A165656 (k=6), A165877 (k=7), A165878 (k=8), A185293 (k=9), A185203 (k=10), A185213 (k=11).
%Y Disconnected 4-regular simple graphs with girth at least g: this sequence (g=3), A185244 (g=4), A185245 (g=5), A185246 (g=6).
%K nonn,nice,hard
%O 0,13
%A Ronald C. Read
%E Terms a(16)-a(18) from _Martin Fuller_, Dec 04 2006
%E Terms a(19)-a(26) from _Jason Kimberley_, Sep 27 2009 and Dec 30 2010
%E Terms a(27)-a(33), due to the extension of A006820 by _Andrew Howroyd_, from _Jason Kimberley_, Mar 12 2020
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